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                    可变参数
            
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                    Recover捕获异常
            
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                    方法
            
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                    方法值和方法表达式
            
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                    示例: Bit数组
            
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                    封装
            
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                    接口
            
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                    接口是合约
            
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                    接口类型
            
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                    实现接口的条件
            
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                    flag.Value接口
            
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                    接口值
            
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                    sort.Interface接口
            
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                    http.Handler接口
            
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                    error接口
            
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                    示例: 表达式求值
            
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                    类型断言
            
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                    基于类型断言识别错误类型
            
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                    通过类型断言查询接口
            
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                    类型分支
            
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                    示例: 基于标记的XML解码
            
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                    补充几点
            
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                    Goroutines和Channels
            
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                    Goroutines
            
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                    示例: 并发的Clock服务
            
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                    示例: 并发的Echo服务
            
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                    Channels
            
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                    并发的循环
            
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                    示例: 并发的Web爬虫
            
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                    基于select的多路复用
            
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                    示例: 并发的目录遍历
            
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        <li class="chapter " data-level="1.9.9" data-path="../ch8/ch8-09.html">
            
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                    并发的退出
            
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                    示例: 聊天服务
            
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        <li class="chapter " data-level="1.10" data-path="../ch9/ch9.html">
            
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                    基于共享变量的并发
            
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                    竞争条件
            
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                    sync.Mutex互斥锁
            
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        <li class="chapter " data-level="1.10.3" data-path="../ch9/ch9-03.html">
            
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                    sync.RWMutex读写锁
            
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                    内存同步
            
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                    sync.Once惰性初始化
            
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                    竞争条件检测
            
                </a>
            

            
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        <li class="chapter " data-level="1.10.7" data-path="../ch9/ch9-07.html">
            
                <a href="../ch9/ch9-07.html">
            
                    
                    示例: 并发的非阻塞缓存
            
                </a>
            

            
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        <li class="chapter " data-level="1.10.8" data-path="../ch9/ch9-08.html">
            
                <a href="../ch9/ch9-08.html">
            
                    
                    Goroutines和线程
            
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            </ul>
            
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        <li class="chapter " data-level="1.11" data-path="../ch10/ch10.html">
            
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                    包和工具
            
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        <li class="chapter " data-level="1.11.1" data-path="../ch10/ch10-01.html">
            
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                    包简介
            
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                    导入路径
            
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                    包声明
            
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        <li class="chapter " data-level="1.11.4" data-path="../ch10/ch10-04.html">
            
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                    导入声明
            
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        <li class="chapter " data-level="1.11.5" data-path="../ch10/ch10-05.html">
            
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                    包的匿名导入
            
                </a>
            

            
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        <li class="chapter " data-level="1.11.6" data-path="../ch10/ch10-06.html">
            
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                    包和命名
            
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                    工具
            
                </a>
            

            
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            </ul>
            
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        <li class="chapter " data-level="1.12" data-path="../ch11/ch11.html">
            
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                    测试
            
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                <a href="../ch11/ch11-01.html">
            
                    
                    go test
            
                </a>
            

            
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        <li class="chapter " data-level="1.12.2" data-path="../ch11/ch11-02.html">
            
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                    测试函数
            
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        <li class="chapter " data-level="1.12.3" data-path="../ch11/ch11-03.html">
            
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                    测试覆盖率
            
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        <li class="chapter " data-level="1.12.4" data-path="../ch11/ch11-04.html">
            
                <a href="../ch11/ch11-04.html">
            
                    
                    基准测试
            
                </a>
            

            
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        <li class="chapter " data-level="1.12.5" data-path="../ch11/ch11-05.html">
            
                <a href="../ch11/ch11-05.html">
            
                    
                    剖析
            
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        <li class="chapter " data-level="1.12.6" data-path="../ch11/ch11-06.html">
            
                <a href="../ch11/ch11-06.html">
            
                    
                    示例函数
            
                </a>
            

            
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            </ul>
            
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        <li class="chapter " data-level="1.13" data-path="../ch12/ch12.html">
            
                <a href="../ch12/ch12.html">
            
                    
                    反射
            
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            <ul class="articles">
                
    
        <li class="chapter " data-level="1.13.1" data-path="../ch12/ch12-01.html">
            
                <a href="../ch12/ch12-01.html">
            
                    
                    为何需要反射?
            
                </a>
            

            
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        <li class="chapter " data-level="1.13.2" data-path="../ch12/ch12-02.html">
            
                <a href="../ch12/ch12-02.html">
            
                    
                    reflect.Type和reflect.Value
            
                </a>
            

            
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        <li class="chapter " data-level="1.13.3" data-path="../ch12/ch12-03.html">
            
                <a href="../ch12/ch12-03.html">
            
                    
                    Display递归打印
            
                </a>
            

            
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        <li class="chapter " data-level="1.13.4" data-path="../ch12/ch12-04.html">
            
                <a href="../ch12/ch12-04.html">
            
                    
                    示例: 编码S表达式
            
                </a>
            

            
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        <li class="chapter " data-level="1.13.5" data-path="../ch12/ch12-05.html">
            
                <a href="../ch12/ch12-05.html">
            
                    
                    通过reflect.Value修改值
            
                </a>
            

            
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        <li class="chapter " data-level="1.13.6" data-path="../ch12/ch12-06.html">
            
                <a href="../ch12/ch12-06.html">
            
                    
                    示例: 解码S表达式
            
                </a>
            

            
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        <li class="chapter " data-level="1.13.7" data-path="../ch12/ch12-07.html">
            
                <a href="../ch12/ch12-07.html">
            
                    
                    获取结构体字段标签
            
                </a>
            

            
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        <li class="chapter " data-level="1.13.8" data-path="../ch12/ch12-08.html">
            
                <a href="../ch12/ch12-08.html">
            
                    
                    显示一个类型的方法集
            
                </a>
            

            
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        <li class="chapter " data-level="1.13.9" data-path="../ch12/ch12-09.html">
            
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                    几点忠告
            
                </a>
            

            
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        <li class="chapter " data-level="1.14" data-path="../ch13/ch13.html">
            
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                    底层编程
            
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        <li class="chapter " data-level="1.14.1" data-path="../ch13/ch13-01.html">
            
                <a href="../ch13/ch13-01.html">
            
                    
                    unsafe.Sizeof, Alignof 和 Offsetof
            
                </a>
            

            
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        <li class="chapter " data-level="1.14.2" data-path="../ch13/ch13-02.html">
            
                <a href="../ch13/ch13-02.html">
            
                    
                    unsafe.Pointer
            
                </a>
            

            
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        <li class="chapter " data-level="1.14.3" data-path="../ch13/ch13-03.html">
            
                <a href="../ch13/ch13-03.html">
            
                    
                    示例: 深度相等判断
            
                </a>
            

            
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        <li class="chapter " data-level="1.14.4" data-path="../ch13/ch13-04.html">
            
                <a href="../ch13/ch13-04.html">
            
                    
                    通过cgo调用C代码
            
                </a>
            

            
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                    几点忠告
            
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        <a href=".." >复数</a>
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                                <h2 id="33-&#x590D;&#x6570;">3.3. &#x590D;&#x6570;</h2>
<p>Go&#x8BED;&#x8A00;&#x63D0;&#x4F9B;&#x4E86;&#x4E24;&#x79CD;&#x7CBE;&#x5EA6;&#x7684;&#x590D;&#x6570;&#x7C7B;&#x578B;&#xFF1A;complex64&#x548C;complex128&#xFF0C;&#x5206;&#x522B;&#x5BF9;&#x5E94;float32&#x548C;float64&#x4E24;&#x79CD;&#x6D6E;&#x70B9;&#x6570;&#x7CBE;&#x5EA6;&#x3002;&#x5185;&#x7F6E;&#x7684;complex&#x51FD;&#x6570;&#x7528;&#x4E8E;&#x6784;&#x5EFA;&#x590D;&#x6570;&#xFF0C;&#x5185;&#x5EFA;&#x7684;real&#x548C;imag&#x51FD;&#x6570;&#x5206;&#x522B;&#x8FD4;&#x56DE;&#x590D;&#x6570;&#x7684;&#x5B9E;&#x90E8;&#x548C;&#x865A;&#x90E8;&#xFF1A;</p>
<pre><code class="lang-Go"><span class="hljs-keyword">var</span> x <span class="hljs-keyword">complex128</span> = <span class="hljs-built_in">complex</span>(<span class="hljs-number">1</span>, <span class="hljs-number">2</span>) <span class="hljs-comment">// 1+2i</span>
<span class="hljs-keyword">var</span> y <span class="hljs-keyword">complex128</span> = <span class="hljs-built_in">complex</span>(<span class="hljs-number">3</span>, <span class="hljs-number">4</span>) <span class="hljs-comment">// 3+4i</span>
fmt.Println(x*y)                 <span class="hljs-comment">// &quot;(-5+10i)&quot;</span>
fmt.Println(<span class="hljs-built_in">real</span>(x*y))           <span class="hljs-comment">// &quot;-5&quot;</span>
fmt.Println(<span class="hljs-built_in">imag</span>(x*y))           <span class="hljs-comment">// &quot;10&quot;</span>
</code></pre>
<p>&#x5982;&#x679C;&#x4E00;&#x4E2A;&#x6D6E;&#x70B9;&#x6570;&#x9762;&#x503C;&#x6216;&#x4E00;&#x4E2A;&#x5341;&#x8FDB;&#x5236;&#x6574;&#x6570;&#x9762;&#x503C;&#x540E;&#x9762;&#x8DDF;&#x7740;&#x4E00;&#x4E2A;i&#xFF0C;&#x4F8B;&#x5982;3.141592i&#x6216;2i&#xFF0C;&#x5B83;&#x5C06;&#x6784;&#x6210;&#x4E00;&#x4E2A;&#x590D;&#x6570;&#x7684;&#x865A;&#x90E8;&#xFF0C;&#x590D;&#x6570;&#x7684;&#x5B9E;&#x90E8;&#x662F;0&#xFF1A;</p>
<pre><code class="lang-Go">fmt.Println(<span class="hljs-number">1i</span> * <span class="hljs-number">1i</span>) <span class="hljs-comment">// &quot;(-1+0i)&quot;, i^2 = -1</span>
</code></pre>
<p>&#x5728;&#x5E38;&#x91CF;&#x7B97;&#x672F;&#x89C4;&#x5219;&#x4E0B;&#xFF0C;&#x4E00;&#x4E2A;&#x590D;&#x6570;&#x5E38;&#x91CF;&#x53EF;&#x4EE5;&#x52A0;&#x5230;&#x53E6;&#x4E00;&#x4E2A;&#x666E;&#x901A;&#x6570;&#x503C;&#x5E38;&#x91CF;&#xFF08;&#x6574;&#x6570;&#x6216;&#x6D6E;&#x70B9;&#x6570;&#x3001;&#x5B9E;&#x90E8;&#x6216;&#x865A;&#x90E8;&#xFF09;&#xFF0C;&#x6211;&#x4EEC;&#x53EF;&#x4EE5;&#x7528;&#x81EA;&#x7136;&#x7684;&#x65B9;&#x5F0F;&#x4E66;&#x5199;&#x590D;&#x6570;&#xFF0C;&#x5C31;&#x50CF;1+2i&#x6216;&#x4E0E;&#x4E4B;&#x7B49;&#x4EF7;&#x7684;&#x5199;&#x6CD5;2i+1&#x3002;&#x4E0A;&#x9762;x&#x548C;y&#x7684;&#x58F0;&#x660E;&#x8BED;&#x53E5;&#x8FD8;&#x53EF;&#x4EE5;&#x7B80;&#x5316;&#xFF1A;</p>
<pre><code class="lang-Go">x := <span class="hljs-number">1</span> + <span class="hljs-number">2i</span>
y := <span class="hljs-number">3</span> + <span class="hljs-number">4i</span>
</code></pre>
<p>&#x590D;&#x6570;&#x4E5F;&#x53EF;&#x4EE5;&#x7528;==&#x548C;!=&#x8FDB;&#x884C;&#x76F8;&#x7B49;&#x6BD4;&#x8F83;&#x3002;&#x53EA;&#x6709;&#x4E24;&#x4E2A;&#x590D;&#x6570;&#x7684;&#x5B9E;&#x90E8;&#x548C;&#x865A;&#x90E8;&#x90FD;&#x76F8;&#x7B49;&#x7684;&#x65F6;&#x5019;&#x5B83;&#x4EEC;&#x624D;&#x662F;&#x76F8;&#x7B49;&#x7684;&#xFF08;&#x8BD1;&#x6CE8;&#xFF1A;&#x6D6E;&#x70B9;&#x6570;&#x7684;&#x76F8;&#x7B49;&#x6BD4;&#x8F83;&#x662F;&#x5371;&#x9669;&#x7684;&#xFF0C;&#x9700;&#x8981;&#x7279;&#x522B;&#x5C0F;&#x5FC3;&#x5904;&#x7406;&#x7CBE;&#x5EA6;&#x95EE;&#x9898;&#xFF09;&#x3002;</p>
<p>math/cmplx&#x5305;&#x63D0;&#x4F9B;&#x4E86;&#x590D;&#x6570;&#x5904;&#x7406;&#x7684;&#x8BB8;&#x591A;&#x51FD;&#x6570;&#xFF0C;&#x4F8B;&#x5982;&#x6C42;&#x590D;&#x6570;&#x7684;&#x5E73;&#x65B9;&#x6839;&#x51FD;&#x6570;&#x548C;&#x6C42;&#x5E42;&#x51FD;&#x6570;&#x3002;</p>
<pre><code class="lang-Go">fmt.Println(cmplx.Sqrt(<span class="hljs-number">-1</span>)) <span class="hljs-comment">// &quot;(0+1i)&quot;</span>
</code></pre>
<p>&#x4E0B;&#x9762;&#x7684;&#x7A0B;&#x5E8F;&#x4F7F;&#x7528;complex128&#x590D;&#x6570;&#x7B97;&#x6CD5;&#x6765;&#x751F;&#x6210;&#x4E00;&#x4E2A;Mandelbrot&#x56FE;&#x50CF;&#x3002;</p>
<p><u><i>gopl.io/ch3/mandelbrot</i></u></p>
<pre><code class="lang-Go"><span class="hljs-comment">// Mandelbrot emits a PNG image of the Mandelbrot fractal.</span>
<span class="hljs-keyword">package</span> main

<span class="hljs-keyword">import</span> (
    <span class="hljs-string">&quot;image&quot;</span>
    <span class="hljs-string">&quot;image/color&quot;</span>
    <span class="hljs-string">&quot;image/png&quot;</span>
    <span class="hljs-string">&quot;math/cmplx&quot;</span>
    <span class="hljs-string">&quot;os&quot;</span>
)


<span class="hljs-keyword">func</span> main() {
    <span class="hljs-keyword">const</span> (
        xmin, ymin, xmax, ymax = <span class="hljs-number">-2</span>, <span class="hljs-number">-2</span>, +<span class="hljs-number">2</span>, +<span class="hljs-number">2</span>
        width, height          = <span class="hljs-number">1024</span>, <span class="hljs-number">1024</span>
    )

    img := image.NewRGBA(image.Rect(<span class="hljs-number">0</span>, <span class="hljs-number">0</span>, width, height))
    <span class="hljs-keyword">for</span> py := <span class="hljs-number">0</span>; py &lt; height; py++ {
        y := <span class="hljs-keyword">float64</span>(py)/height*(ymax-ymin) + ymin
        <span class="hljs-keyword">for</span> px := <span class="hljs-number">0</span>; px &lt; width; px++ {
            x := <span class="hljs-keyword">float64</span>(px)/width*(xmax-xmin) + xmin
            z := <span class="hljs-built_in">complex</span>(x, y)
            <span class="hljs-comment">// Image point (px, py) represents complex value z.</span>
            img.Set(px, py, mandelbrot(z))
        }
    }
    png.Encode(os.Stdout, img) <span class="hljs-comment">// <span class="hljs-doctag">NOTE:</span> ignoring errors</span>
}

<span class="hljs-keyword">func</span> mandelbrot(z <span class="hljs-keyword">complex128</span>) color.Color {
    <span class="hljs-keyword">const</span> iterations = <span class="hljs-number">200</span>
    <span class="hljs-keyword">const</span> contrast = <span class="hljs-number">15</span>

    <span class="hljs-keyword">var</span> v <span class="hljs-keyword">complex128</span>
    <span class="hljs-keyword">for</span> n := <span class="hljs-keyword">uint8</span>(<span class="hljs-number">0</span>); n &lt; iterations; n++ {
        v = v*v + z
        <span class="hljs-keyword">if</span> cmplx.Abs(v) &gt; <span class="hljs-number">2</span> {
            <span class="hljs-keyword">return</span> color.Gray{<span class="hljs-number">255</span> - contrast*n}
        }
    }
    <span class="hljs-keyword">return</span> color.Black
}
</code></pre>
<p>&#x7528;&#x4E8E;&#x904D;&#x5386;1024x1024&#x56FE;&#x50CF;&#x6BCF;&#x4E2A;&#x70B9;&#x7684;&#x4E24;&#x4E2A;&#x5D4C;&#x5957;&#x7684;&#x5FAA;&#x73AF;&#x5BF9;&#x5E94;-2&#x5230;+2&#x533A;&#x95F4;&#x7684;&#x590D;&#x6570;&#x5E73;&#x9762;&#x3002;&#x7A0B;&#x5E8F;&#x53CD;&#x590D;&#x6D4B;&#x8BD5;&#x6BCF;&#x4E2A;&#x70B9;&#x5BF9;&#x5E94;&#x590D;&#x6570;&#x503C;&#x5E73;&#x65B9;&#x503C;&#x52A0;&#x4E00;&#x4E2A;&#x589E;&#x91CF;&#x503C;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x662F;&#x5426;&#x8D85;&#x51FA;&#x534A;&#x5F84;&#x4E3A;2&#x7684;&#x5706;&#x3002;&#x5982;&#x679C;&#x8D85;&#x8FC7;&#x4E86;&#xFF0C;&#x901A;&#x8FC7;&#x6839;&#x636E;&#x9884;&#x8BBE;&#x7F6E;&#x7684;&#x9003;&#x9038;&#x8FED;&#x4EE3;&#x6B21;&#x6570;&#x5BF9;&#x5E94;&#x7684;&#x7070;&#x5EA6;&#x989C;&#x8272;&#x6765;&#x4EE3;&#x66FF;&#x3002;&#x5982;&#x679C;&#x4E0D;&#x662F;&#xFF0C;&#x90A3;&#x4E48;&#x8BE5;&#x70B9;&#x5C5E;&#x4E8E;Mandelbrot&#x96C6;&#x5408;&#xFF0C;&#x4F7F;&#x7528;&#x9ED1;&#x8272;&#x989C;&#x8272;&#x6807;&#x8BB0;&#x3002;&#x6700;&#x7EC8;&#x7A0B;&#x5E8F;&#x5C06;&#x751F;&#x6210;&#x7684;PNG&#x683C;&#x5F0F;&#x5206;&#x5F62;&#x56FE;&#x50CF;&#x8F93;&#x51FA;&#x5230;&#x6807;&#x51C6;&#x8F93;&#x51FA;&#xFF0C;&#x5982;&#x56FE;3.3&#x6240;&#x793A;&#x3002;</p>
<p><img src="../images/ch3-03.png" alt=""></p>
<p><strong>&#x7EC3;&#x4E60; 3.5&#xFF1A;</strong> &#x5B9E;&#x73B0;&#x4E00;&#x4E2A;&#x5F69;&#x8272;&#x7684;Mandelbrot&#x56FE;&#x50CF;&#xFF0C;&#x4F7F;&#x7528;image.NewRGBA&#x521B;&#x5EFA;&#x56FE;&#x50CF;&#xFF0C;&#x4F7F;&#x7528;color.RGBA&#x6216;color.YCbCr&#x751F;&#x6210;&#x989C;&#x8272;&#x3002;</p>
<p><strong>&#x7EC3;&#x4E60; 3.6&#xFF1A;</strong> &#x5347;&#x91C7;&#x6837;&#x6280;&#x672F;&#x53EF;&#x4EE5;&#x964D;&#x4F4E;&#x6BCF;&#x4E2A;&#x50CF;&#x7D20;&#x5BF9;&#x8BA1;&#x7B97;&#x989C;&#x8272;&#x503C;&#x548C;&#x5E73;&#x5747;&#x503C;&#x7684;&#x5F71;&#x54CD;&#x3002;&#x7B80;&#x5355;&#x7684;&#x65B9;&#x6CD5;&#x662F;&#x5C06;&#x6BCF;&#x4E2A;&#x50CF;&#x7D20;&#x5206;&#x6210;&#x56DB;&#x4E2A;&#x5B50;&#x50CF;&#x7D20;&#xFF0C;&#x5B9E;&#x73B0;&#x5B83;&#x3002;</p>
<p><strong>&#x7EC3;&#x4E60; 3.7&#xFF1A;</strong> &#x53E6;&#x4E00;&#x4E2A;&#x751F;&#x6210;&#x5206;&#x5F62;&#x56FE;&#x50CF;&#x7684;&#x65B9;&#x5F0F;&#x662F;&#x4F7F;&#x7528;&#x725B;&#x987F;&#x6CD5;&#x6765;&#x6C42;&#x89E3;&#x4E00;&#x4E2A;&#x590D;&#x6570;&#x65B9;&#x7A0B;&#xFF0C;&#x4F8B;&#x5982;$z^4-1=0$&#x3002;&#x6BCF;&#x4E2A;&#x8D77;&#x70B9;&#x5230;&#x56DB;&#x4E2A;&#x6839;&#x7684;&#x8FED;&#x4EE3;&#x6B21;&#x6570;&#x5BF9;&#x5E94;&#x9634;&#x5F71;&#x7684;&#x7070;&#x5EA6;&#x3002;&#x65B9;&#x7A0B;&#x6839;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x7528;&#x989C;&#x8272;&#x8868;&#x793A;&#x3002;</p>
<p><strong>&#x7EC3;&#x4E60; 3.8&#xFF1A;</strong> &#x901A;&#x8FC7;&#x63D0;&#x9AD8;&#x7CBE;&#x5EA6;&#x6765;&#x751F;&#x6210;&#x66F4;&#x591A;&#x7EA7;&#x522B;&#x7684;&#x5206;&#x5F62;&#x3002;&#x4F7F;&#x7528;&#x56DB;&#x79CD;&#x4E0D;&#x540C;&#x7CBE;&#x5EA6;&#x7C7B;&#x578B;&#x7684;&#x6570;&#x5B57;&#x5B9E;&#x73B0;&#x76F8;&#x540C;&#x7684;&#x5206;&#x5F62;&#xFF1A;complex64&#x3001;complex128&#x3001;big.Float&#x548C;big.Rat&#x3002;&#xFF08;&#x540E;&#x9762;&#x4E24;&#x79CD;&#x7C7B;&#x578B;&#x5728;math/big&#x5305;&#x58F0;&#x660E;&#x3002;Float&#x662F;&#x6709;&#x6307;&#x5B9A;&#x9650;&#x7CBE;&#x5EA6;&#x7684;&#x6D6E;&#x70B9;&#x6570;&#xFF1B;Rat&#x662F;&#x65E0;&#x9650;&#x7CBE;&#x5EA6;&#x7684;&#x6709;&#x7406;&#x6570;&#x3002;&#xFF09;&#x5B83;&#x4EEC;&#x95F4;&#x7684;&#x6027;&#x80FD;&#x548C;&#x5185;&#x5B58;&#x4F7F;&#x7528;&#x5BF9;&#x6BD4;&#x5982;&#x4F55;&#xFF1F;&#x5F53;&#x6E32;&#x67D3;&#x56FE;&#x53EF;&#x89C1;&#x65F6;&#x7F29;&#x653E;&#x7684;&#x7EA7;&#x522B;&#x662F;&#x591A;&#x5C11;&#xFF1F;</p>
<p><strong>&#x7EC3;&#x4E60; 3.9&#xFF1A;</strong> &#x7F16;&#x5199;&#x4E00;&#x4E2A;web&#x670D;&#x52A1;&#x5668;&#xFF0C;&#x7528;&#x4E8E;&#x7ED9;&#x5BA2;&#x6237;&#x7AEF;&#x751F;&#x6210;&#x5206;&#x5F62;&#x7684;&#x56FE;&#x50CF;&#x3002;&#x8FD0;&#x884C;&#x5BA2;&#x6237;&#x7AEF;&#x901A;&#x8FC7;HTTP&#x53C2;&#x6570;&#x6307;&#x5B9A;x&#x3001;y&#x548C;zoom&#x53C2;&#x6570;&#x3002;</p>

                                
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